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Aspherical gravitational monopoles
Alain Connes, Thibault Damour, Pierre Fayet
We show how to construct non-spherically-symmetric extended bodies of uniform density behaving exactly as pointlike masses. These ``gravitational monopoles'' have the following equ…
A Universal Action Formula
Ali Chamseddine, Alain Connes
A universal formula for an action associated with a noncommutative geometry, defined by a spectal triple $(\Ac ,\Hc ,D)$, is proposed. It is based on the spectrum of the Dirac oper…
The Spectral Action Principle
Ali H. Chamseddine, Alain Connes
We propose a new action principle to be associated with a noncommutative space $(\Ac ,\Hc ,D)$. The universal formula for the spectral action is $(ψ,Dψ) + \Trace (χ(D /$ $\Lb))$ wh…
Gravity coupled with matter and foundation of non-commutative geometry
A. Connes
We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element . Its unitary repres…